Abstract
We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus translating the task into an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct analytical solution, providing at the same time a high degree of flexibility over the types of gate-design problems that can be approached. As a significant example, we find generators for the Toffoli gate using only diagonal pairwise interactions, which are easier to implement in some experimental architectures. To showcase the flexibility of the supervised learning approach, we give an example of a non-trivial four-qubit gate that is implementable using only diagonal, pairwise interactions.
Highlights
Let us consider the synthesis of a quantum operation G from the underlying dynamics of a quantum system
We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions
We present an extensive exploration of training scenarios with more restrictive sets of interactions, finding approximate generators for Toffoli and Fredkin gates with good fidelities
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Luca Innocenti1 , Leonardo Banchi2,3,4,5 , Alessandro Ferraro1 , Sougato Bose3 and Mauro Paternostro1,6 Keywords: machine learning, quantum circuits, quantum computing, supervised learning
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